1 Effect of UPSTM-Based Decorrelation on Feature Discovery

1.0.1 Loading the libraries

library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)
library(mlbench)
library(psych)
library(whitening)
library("vioplot")
library("rpart")

op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)

1.1 Material and Methods

mlBench library

Newman, D.J. & Hettich, S. & Blake, C.L. & Merz, C.J. (1998). UCI Repository of machine learning databases [http://www.ics.uci.edu/~mlearn/MLRepository.html]. Irvine, CA: University of California, Department of Information and Computer Science.

1.2 The Data

#data(PimaIndiansDiabetes)
#pander::pander(table(PimaIndiansDiabetes$diabetes))
#PimaIndiansDiabetes$diabetes <- 1*(PimaIndiansDiabetes$diabetes=="pos")

data("PimaIndiansDiabetes2", package = "mlbench")
PimaIndiansDiabetes  <- PimaIndiansDiabetes2[complete.cases(PimaIndiansDiabetes2),]


#data(PimaIndiansDiabetes)
#PimaIndiansDiabetes  <- PimaIndiansDiabetes[complete.cases(PimaIndiansDiabetes),]


PimaIndiansDiabetes_mat <- as.data.frame(model.matrix(diabetes~.*.,PimaIndiansDiabetes)[,-1])
fnames <- colnames(PimaIndiansDiabetes_mat)
fnames <- str_replace_all(fnames," ","_")
fnames <- str_replace_all(fnames,"/","_")
fnames <- str_replace_all(fnames,":","_x_")
colnames(PimaIndiansDiabetes_mat) <- fnames

whohasx <- str_detect(fnames,"_x_")
PimaIndiansDiabetes_mat[,whohasx] <- sqrt(PimaIndiansDiabetes_mat[,whohasx])

pander::pander(table(PimaIndiansDiabetes$diabetes))
neg pos
262 130
PimaIndiansDiabetes_mat$diabetes <- 1*(PimaIndiansDiabetes$diabetes=="pos")

1.2.0.1 Standarize the names for the reporting

studyName <- "Diabetes"
dataframe <- PimaIndiansDiabetes_mat
outcome <- "diabetes"

thro <- 0.6
TopVariables <- 5
cexheat = 0.35

1.3 Generaring the report

1.3.1 Libraries

Some libraries

library(psych)
library(whitening)
library("vioplot")
library("rpart")

1.3.2 Data specs

pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))
rows col
392 36
pander::pander(table(dataframe[,outcome]))
0 1
262 130

varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]

largeSet <- length(varlist) > 1500 

1.3.3 Scaling the data

Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns


  ### Some global cleaning
  sdiszero <- apply(dataframe,2,sd) > 1.0e-16
  dataframe <- dataframe[,sdiszero]

  varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
  tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
  dataframe <- dataframe[,tokeep]

  varlist <- colnames(dataframe)
  varlist <- varlist[varlist != outcome]
  
  iscontinous <- sapply(apply(dataframe,2,unique),length) >= 5 ## Only variables with enough samples



dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData

1.4 The heatmap of the data

numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000


if (!largeSet)
{

  hm <- heatMaps(data=dataframeScaled[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 xlab="Feature",
                 ylab="Sample",
                 srtCol=45,
                 srtRow=45,
                 cexCol=cexheat,
                 cexRow=cexheat
                 )
  par(op)
}

1.4.0.1 Correlation Matrix of the Data

The heat map of the data


if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  #cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
  cormat <- cor(dataframe[,varlist],method="pearson")
  cormat[is.na(cormat)] <- 0
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Original Correlation",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.9815674

1.5 The decorrelation


DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#> 
#>  pregnant_x_pressure 
#>   pregnant    glucose   pressure    triceps    insulin       mass 
#> 0.86111111 0.19444444 0.02777778 0.69444444 0.77777778 0.25000000 
#> 
#>  Included: 36 , Uni p: 0.004166667 , Base Size: 1 , Rcrit: 0.1330839 
#> 
#> 
 1 <R=0.910,thr=0.950>, Top: 4< 4 >[Fa= 4 ]( 4 , 7 , 0 ),<|><>Tot Used: 11 , Added: 7 , Zero Std: 0 , Max Cor: 0.945
#> 
 2 <R=0.864,thr=0.900>, Top: 4< 2 >[Fa= 6 ]( 4 , 8 , 4 ),<|><>Tot Used: 20 , Added: 8 , Zero Std: 0 , Max Cor: 0.939
#> 
 3 <R=0.826,thr=0.900>, Top: 1< 1 >[Fa= 7 ]( 1 , 1 , 6 ),<|><>Tot Used: 21 , Added: 1 , Zero Std: 0 , Max Cor: 0.898
#> 
 4 <R=0.812,thr=0.800>, Top: 7< 3 >[Fa= 9 ]( 7 , 14 , 7 ),<|><>Tot Used: 33 , Added: 14 , Zero Std: 0 , Max Cor: 0.974
#> 
 5 <R=0.821,thr=0.950>, Top: 2< 1 >[Fa= 11 ]( 2 , 2 , 9 ),<|><>Tot Used: 33 , Added: 2 , Zero Std: 0 , Max Cor: 0.930
#> 
 6 <R=0.789,thr=0.900>, Top: 2< 1 >[Fa= 11 ]( 2 , 2 , 11 ),<|><>Tot Used: 33 , Added: 2 , Zero Std: 0 , Max Cor: 0.873
#> 
 7 <R=0.768,thr=0.800>, Top: 4< 1 >[Fa= 11 ]( 3 , 5 , 11 ),<|><>Tot Used: 33 , Added: 5 , Zero Std: 0 , Max Cor: 0.894
#> 
 8 <R=0.738,thr=0.800>, Top: 1< 2 >[Fa= 11 ]( 1 , 2 , 11 ),<|><>Tot Used: 33 , Added: 2 , Zero Std: 0 , Max Cor: 0.793
#> 
 9 <R=0.720,thr=0.700>, Top: 9< 3 >[Fa= 11 ]( 7 , 11 , 11 ),<|><>Tot Used: 36 , Added: 11 , Zero Std: 0 , Max Cor: 0.918
#> 
 10 <R=0.757,thr=0.900>, Top: 1< 1 >[Fa= 11 ]( 1 , 1 , 11 ),<|><>Tot Used: 36 , Added: 1 , Zero Std: 0 , Max Cor: 0.832
#> 
 11 <R=0.737,thr=0.800>, Top: 4< 2 >[Fa= 11 ]( 4 , 5 , 11 ),<|><>Tot Used: 36 , Added: 5 , Zero Std: 0 , Max Cor: 0.767
#> 
 12 <R=0.676,thr=0.700>, Top: 2< 1 >[Fa= 11 ]( 2 , 2 , 11 ),<|><>Tot Used: 36 , Added: 2 , Zero Std: 0 , Max Cor: 0.740
#> 
 13 <R=0.666,thr=0.700>, Top: 1< 1 >[Fa= 12 ]( 1 , 1 , 11 ),<|><>Tot Used: 36 , Added: 1 , Zero Std: 0 , Max Cor: 0.679
#> 
 14 <R=0.650,thr=0.600>, Top: 4< 3 >[Fa= 13 ]( 4 , 6 , 12 ),<|><>Tot Used: 36 , Added: 6 , Zero Std: 0 , Max Cor: 0.784
#> 
 15 <R=0.784,thr=0.700>, Top: 1< 1 >[Fa= 13 ]( 1 , 1 , 13 ),<|><>Tot Used: 36 , Added: 1 , Zero Std: 0 , Max Cor: 0.685
#> 
 16 <R=0.685,thr=0.600>, Top: 1< 1 >[Fa= 13 ]( 1 , 1 , 13 ),<|><>Tot Used: 36 , Added: 1 , Zero Std: 0 , Max Cor: 0.625
#> 
 17 <R=0.625,thr=0.600>, Top: 1< 1 >[Fa= 13 ]( 1 , 1 , 13 ),<|><>Tot Used: 36 , Added: 1 , Zero Std: 0 , Max Cor: 0.598
#> 
 18 <R=0.598,thr=0.600>
#> 
 [ 18 ], 0.5981508 Decor Dimension: 36 Nused: 36 . Cor to Base: 27 , ABase: 36 , Outcome Base: 0 
#> 
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]

pander::pander(sum(apply(dataframe[,varlist],2,var)))

24490

pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))

4922

pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))

3.45

pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))

3.09


varratio <- attr(DEdataframe,"VarRatio")

pander::pander(tail(varratio))
La_mass_x_age La_pregnant_x_mass La_mass La_glucose_x_triceps La_pregnant_x_age La_glucose_x_age
0.0186 0.0184 0.0138 0.0133 0.0109 0.00587

1.5.1 The decorrelation matrix


if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  
  UPLTM <- attr(DEdataframe,"UPLTM")
  
  gplots::heatmap.2(1.0*(abs(UPLTM)>0),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Decorrelation matrix",
                    cexRow = cexheat,
                    cexCol = cexheat,
                   srtCol=45,
                   srtRow=45,
                    key.title=NA,
                    key.xlab="|Beta|>0",
                    xlab="Output Feature", ylab="Input Feature")
  
  par(op)
  
  
  
}

1.5.2 Formulas Network

Displaying the features associations

par(op)
clustable <- c("To many variables")


  transform <- attr(DEdataframe,"UPLTM") != 0
  tnames <- colnames(transform)
  colnames(transform) <- str_remove_all(colnames(transform),"La_")
  transform <- abs(transform*cor(dataframe[,rownames(transform)])) # The weights are proportional to the observed correlation
  
  
  fscore <- attr(DEdataframe,"fscore")
  VertexSize <- fscore # The size depends on the variable independence relevance (fscore)
  names(VertexSize) <- str_remove_all(names(VertexSize),"La_")
  VertexSize <- 10*(VertexSize-min(VertexSize))/(max(VertexSize)-min(VertexSize)) # Normalization

  VertexSize <- VertexSize[rownames(transform)]
  rsum <- apply(1*(transform !=0),1,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
  csum <- apply(1*(transform !=0),2,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
  
  ntop <- min(10,length(rsum))


  topfeatures <- unique(c(names(rsum[order(-rsum)])[1:ntop],names(csum[order(-csum)])[1:ntop]))
  rtrans <- transform[topfeatures,]
  csum <- (apply(1*(rtrans !=0),2,sum) > 1*(colnames(rtrans) %in% topfeatures))
  rtrans <- rtrans[,csum]
  topfeatures <- unique(c(topfeatures,colnames(rtrans)))
  print(ncol(transform))

[1] 36

  transform <- transform[topfeatures,topfeatures]
  print(ncol(transform))

[1] 36

  if (ncol(transform)>100)
  {
    csum <- apply(1*(transform !=0),1,sum) 
    csum <- csum[csum > 1]
    csum <- csum + 0.01*VertexSize[names(csum)]
    csum <- csum[order(-csum)]
    tpsum <- min(20,length(csum))
    trsum <- rownames(transform)[rownames(transform) %in% names(csum[1:tpsum])]
    rtrans <- transform[trsum,]
    topfeatures <- unique(c(rownames(rtrans),colnames(rtrans)))
    transform <- transform[topfeatures,topfeatures]
    if (nrow(transform) > 150)
    {
      csum <- apply(1*(rtrans != 0 ),2,sum)
      csum <- csum + 0.01*VertexSize[names(csum)]
      csum <- csum[order(-csum)]
      tpsum <- min(130,length(csum))
      csum <- rownames(transform)[rownames(transform) %in% names(csum[1:tpsum])]
      csum <- unique(c(trsum,csum))
      transform <- transform[csum,csum]
    }
    print(ncol(transform))
  }

    if (ncol(transform) < 150)
    {

      gplots::heatmap.2(transform,
                        trace = "none",
                        mar = c(5,5),
                        col=rev(heat.colors(5)),
                        main = "Red Decorrelation matrix",
                        cexRow = cexheat,
                        cexCol = cexheat,
                       srtCol=45,
                       srtRow=45,
                        key.title=NA,
                        key.xlab="|Beta|>0",
                        xlab="Output Feature", ylab="Input Feature")
  
      par(op)
      VertexSize <- VertexSize[colnames(transform)]
      gr <- graph_from_adjacency_matrix(transform,mode = "directed",diag = FALSE,weighted=TRUE)
      gr$layout <- layout_with_fr
      
#      fc <- cluster_optimal(gr)
        fc <- cluster_walktrap (gr,steps=50)
      plot(fc, gr,
           edge.width = 2*E(gr)$weight,
           vertex.size=VertexSize,
           edge.arrow.size=0.5,
           edge.arrow.width=0.5,
           vertex.label.cex=(0.15+0.05*VertexSize),
           vertex.label.dist=0.5 + 0.05*VertexSize,
           main="Top Feature Association")
      
      varratios <- varratio
      fscores <- fscore
      names(varratios) <- str_remove_all(names(varratios),"La_")
      names(fscores) <- str_remove_all(names(fscores),"La_")

      dc <- getLatentCoefficients(DEdataframe)
      theCharformulas <- attr(dc,"LatentCharFormulas")

      
      clustable <- as.data.frame(cbind(Variable=fc$names,
                                       Formula=as.character(theCharformulas[paste("La_",fc$names,sep="")]),
                                       Class=fc$membership,
                                       ResidualVariance=round(varratios[fc$names],3),
                                       Fscore=round(fscores[fc$names],3)
                                       )
                                 )
      rownames(clustable) <- str_replace_all(rownames(clustable),"__","_")
      clustable$Variable <- NULL
      clustable$Class <- as.integer(clustable$Class)
      clustable$ResidualVariance <- as.numeric(clustable$ResidualVariance)
      clustable$Fscore <- as.numeric(clustable$Fscore)
      clustable <- clustable[order(-clustable$Fscore),]
      clustable <- clustable[order(clustable$Class),]
      clustable <- clustable[clustable$Fscore >= -1,]
      topv <- min(50,nrow(clustable))
      clustable <- clustable[1:topv,]
    }


pander::pander(clustable)
  Formula Class ResidualVariance Fscore
triceps_x_mass NA 1 1.000 13
glucose_x_insulin NA 1 1.000 8
glucose + glucose - (0.393)glucose_x_insulin 1 0.420 5
triceps + triceps - (1.217)triceps_x_mass 1 0.091 5
age + age - (0.790)pregnant_x_pressure 2 0.582 8
pregnant_x_pressure NA 2 1.000 8
pressure_x_age - (0.836)age + pressure_x_age 2 0.182 3
pregnant_x_glucose + pregnant_x_glucose - (1.303)pregnant_x_pressure 2 0.057 0
pregnant_x_age - (0.284)age - (0.639)pregnant_x_pressure + pregnant_x_age + (0.158)pressure_x_age 2 0.011 -1
mass_x_pedigree NA 3 1.000 7
pressure_x_insulin + pressure_x_insulin - (1.319)insulin_x_mass 3 0.085 2
insulin_x_mass - (0.425)glucose_x_insulin + insulin_x_mass 3 0.106 1

par(op)

1.6 The heatmap of the decorrelated data

if (!largeSet)
{

  hm <- heatMaps(data=DEdataframe[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 cexRow = cexheat,
                 cexCol = cexheat,
                 srtCol=45,
                 srtRow=45,
                 xlab="Feature",
                 ylab="Sample")
  par(op)
}

1.7 The correlation matrix after decorrelation

if (!largeSet)
{

  cormat <- cor(DEdataframe[,varlistc],method="pearson")
  cormat[is.na(cormat)] <- 0
  
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Correlation after ILAA",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  
  par(op)
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.5981508

1.8 U-MAP Visualization of features

1.8.1 The UMAP on Raw Data


  classes <- unique(dataframe[1:numsub,outcome])
  raincolors <- rainbow(length(classes))
  names(raincolors) <- classes
  topvars <- univariate_BinEnsemble(dataframe,outcome)
  lso <- LASSO_MIN(formula(paste(outcome,"~.")),dataframe,family="binomial")
  topvars <- unique(c(names(topvars),lso$selectedfeatures))
  pander::pander(head(topvars))

glucose, glucose_x_pressure, glucose_x_triceps, glucose_x_mass, glucose_x_age and insulin_x_age

#  names(topvars)
#if (nrow(dataframe) < 1000)
#{
  datasetframe.umap = umap(scale(dataframe[1:numsub,topvars]),n_components=2)
#  datasetframe.umap = umap(dataframe[1:numsub,varlist],n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
  text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])

#}

1.8.2 The decorralted UMAP

  varlistcV <- names(varratio[varratio >= 0.01])
  topvars <- univariate_BinEnsemble(DEdataframe[,varlistcV],outcome)
  lso <- LASSO_MIN(formula(paste(outcome,"~.")),DEdataframe[,varlistcV],family="binomial")
  topvars <- unique(c(names(topvars),lso$selectedfeatures))
  pander::pander(head(topvars))

La_insulin_x_pedigree, La_glucose_x_mass, glucose_x_insulin, La_glucose, La_pregnant_x_glucose and La_triceps_x_insulin


  varlistcV <- varlistcV[varlistcV != outcome]
  
#  DEdataframe[,outcome] <- as.numeric(DEdataframe[,outcome])
#if (nrow(dataframe) < 1000)
#{
  datasetframe.umap = umap(scale(DEdataframe[1:numsub,topvars]),n_components=2)
#  datasetframe.umap = umap(DEdataframe[1:numsub,varlistcV],n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After ILAA",t='n')
  text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])

#}

1.9 Univariate Analysis

1.9.1 Univariate



univarRAW <- uniRankVar(varlist,
               paste(outcome,"~1"),
               outcome,
               dataframe,
               rankingTest="AUC")



univarDe <- uniRankVar(varlistc,
               paste(outcome,"~1"),
               outcome,
               DEdataframe,
               rankingTest="AUC",
               )

1.9.2 Final Table


univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")

##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)
  caseMean caseStd controlMean controlStd controlKSP ROCAUC
glucose_x_age 71.3 14.04 55.5 11.26 0.000494 0.825
glucose_x_mass 71.4 9.81 58.9 9.73 0.706132 0.821
glucose 145.2 29.84 111.4 24.64 0.034320 0.806
glucose_x_pressure 102.8 14.77 86.9 13.16 0.257647 0.793
glucose_x_triceps 68.1 12.85 53.9 12.77 0.421846 0.784


topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]


pander::pander(finalTable)
  caseMean caseStd controlMean controlStd controlKSP ROCAUC
glucose_x_insulin 167.20 60.56 116.02 51.83 0.009684 0.768
La_insulin_x_pedigree -6.72 1.93 -5.56 1.32 0.038723 0.739
La_glucose_x_mass -4.77 1.92 -3.47 1.69 0.000224 0.719
La_glucose 79.54 23.96 65.88 15.90 0.075929 0.686
La_triceps_x_insulin -32.45 8.44 -27.75 6.34 0.070954 0.685

dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")


pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))
mean total fraction
3.44 32 0.889

theCharformulas <- attr(dc,"LatentCharFormulas")

topvar <- rownames(tableRaw)
finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])


orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]
finalTable$varratio <- varratio[rownames(finalTable)]

Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores","varratio")

finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])
  DecorFormula caseMean caseStd controlMean controlStd controlKSP ROCAUC RAWAUC fscores varratio
glucose_x_age NA 71.29 14.04 55.49 11.26 0.000494 0.825 0.825 NA NA
glucose_x_mass NA 71.37 9.81 58.90 9.73 0.706132 0.821 0.821 NA NA
glucose NA 145.19 29.84 111.43 24.64 0.034320 0.806 0.806 NA NA
glucose_x_pressure NA 102.83 14.77 86.94 13.16 0.257647 0.793 0.793 NA NA
glucose_x_triceps NA 68.06 12.85 53.86 12.77 0.421846 0.784 0.784 NA NA
glucose_x_insulin NA 167.20 60.56 116.02 51.83 0.009684 0.768 0.768 8 1.0000
La_insulin_x_pedigree - (0.055)glucose_x_insulin + insulin_x_pedigree - (1.743)mass_x_pedigree -6.72 1.93 -5.56 1.32 0.038723 0.739 0.742 -2 0.1387
La_glucose_x_mass - (0.303)glucose + (0.924)age + glucose_x_mass - (1.853)mass_x_age -4.77 1.92 -3.47 1.69 0.000224 0.719 0.821 -2 0.0269
La_glucose + glucose - (0.393)glucose_x_insulin 79.54 23.96 65.88 15.90 0.075929 0.686 0.806 5 0.4197
La_triceps_x_insulin - (0.412)glucose_x_insulin + triceps_x_insulin - (1.229)triceps_x_mass -32.45 8.44 -27.75 6.34 0.070954 0.685 0.753 -2 0.0721

1.10 Comparing ILAA vs PCA vs EFA

1.10.1 PCA

featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE,tol=0.01)   #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous]) 
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)

#pander::pander(pc$rotation)


PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])


  gplots::heatmap.2(abs(PCACor),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "PCA Correlation",
                    cexRow = 0.5,
                    cexCol = 0.5,
                     srtCol=45,
                     srtRow= -45,
                    key.title=NA,
                    key.xlab="Pearson Correlation",
                    xlab="Feature", ylab="Feature")

1.10.2 EFA


EFAdataframe <- dataframeScaled

if (length(iscontinous) < 2000)
{
  topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)-1)
  if (topred < 2) topred <- 2
  
  uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE)  # EFA analysis
  predEFA <- predict(uls,dataframeScaled[,iscontinous])
  EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
  colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous]) 


  
  EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
  
  
    gplots::heatmap.2(abs(EFACor),
                      trace = "none",
    #                  scale = "row",
                      mar = c(5,5),
                      col=rev(heat.colors(5)),
                      main = "EFA Correlation",
                      cexRow = 0.5,
                      cexCol = 0.5,
                       srtCol=45,
                       srtRow= -45,
                      key.title=NA,
                      key.xlab="Pearson Correlation",
                      xlab="Feature", ylab="Feature")
}

1.11 Effect on CAR modeling

par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(rawmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
  }


pander::pander(table(dataframe[,outcome],pr))
  0 1
0 220 42
1 31 99
pander::pander(ptab$detail[c(5,3,4,6),])
  statistic est lower upper
5 diag.ac 0.814 0.772 0.851
3 se 0.762 0.679 0.832
4 sp 0.840 0.790 0.882
6 diag.or 16.728 9.933 28.171

par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe[,c(outcome,varlistcV)],control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(IDeAmodel,main="ILAA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(IDeAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
  }

pander::pander(table(DEdataframe[,outcome],pr))
  0 1
0 219 43
1 31 99
pander::pander(ptab$detail[c(5,3,4,6),])
  statistic est lower upper
5 diag.ac 0.811 0.769 0.849
3 se 0.762 0.679 0.832
4 sp 0.836 0.785 0.879
6 diag.or 16.265 9.677 27.337

par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
  plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
  text(PCAmodel, use.n = TRUE,cex=0.75)
  ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}

pander::pander(table(PCAdataframe[,outcome],pr))
  0 1
0 217 45
1 23 107
pander::pander(ptab$detail[c(5,3,4,6),])
  statistic est lower upper
5 diag.ac 0.827 0.785 0.863
3 se 0.823 0.746 0.884
4 sp 0.828 0.777 0.872
6 diag.or 22.434 12.902 39.007


par(op)

1.11.1 EFA


  EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
  EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
  pr <- predict(EFAmodel,EFAdataframe,type = "class")
  
  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(EFAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
  }


  pander::pander(table(EFAdataframe[,outcome],pr))
  0 1
0 244 18
1 56 74
  pander::pander(ptab$detail[c(5,3,4,6),])
  statistic est lower upper
5 diag.ac 0.811 0.769 0.849
3 se 0.569 0.480 0.656
4 sp 0.931 0.894 0.959
6 diag.or 17.913 9.916 32.357
  par(op)